A note on grammars with regular restrictions

A context-free e-free grammar with regular restrictions is a context-free £-free grammar G over which a context-free rule r or G is applicable on a string x only if x e y(r) where y(r) is a regular set. It is known from [1] that the context-free £-free grammars with regular restrictions are as powerful as Chomsky's grammars of the type 0. It is shown, that the same result holds for the grammars, for which the condition x £ y(r) is replaced by the condition x e y where y is a regular set associated with the whole grammar (i.e. independent on the rule r to be applied).